Providenciales has several good supermarkets located across the island. These stores stock primarily American products, but there is a wide range of world-foods available.
For those staying in Grace Bay, the Graceway Gourmet supermarket is located within walking distance of most hotels and resorts. There food selection is more limited than it's parent supermarket Graceway IGA located on Leeward Highway, but this store also carries a wide selection of wines and other specialty products.
There's also a few wholesale supermarkets located in Leeward Highway and the Downtown areas of Providenciales.
Unlike in some American states, there's no law against selling alcohol (including wines and liquors) at grocery stores. However, it should be noted that alcohol sales are prohibited on Sundays (it's still possible to purchase alcohol on Sunday in bars and restaurants).
The majority of supermarkets also sell beer, wind and spirits.